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On finitely Lipschitz space mappings

R. R. Salimov

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk

Abstract: It is established that a ring $Q$-homeomorphism with respect to $p$-modulus in $\mathbb R^n$, $n\geqslant2$, is finitely Lipschitz if $n-1<p<n$ and if the mean integral value of $Q(x)$ over infinitesimal balls $B(x_0,\varepsilon)$ is finite everywhere.

Keywords: $Q$-homeomorphisms, $p$-modulus, $p$-capacity, finite Lipschitz.

UDC: 517.5

MSC: 30C65, 30C75

Received May 23, 2011, published September 28, 2011

Language: English